We can use projectRaster() to transform the CRS of one spatial object to match another spatial object
st_crs(LU_val)[[2]] # to retrieve the proj4string
## [1] "+proj=tmerc +lat_0=0 +lon_0=-73.5 +k=0.9999 +x_0=304800 +y_0=0 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs"
alt_proj <- projectRaster(alt_crop, crs = st_crs(LU_val)[[2]])
alt_proj
## class : RasterLayer
## dimensions : 48, 72, 3456 (nrow, ncol, ncell)
## resolution : 650, 926 (x, y)
## extent : 263713, 310513, 5025305, 5069753 (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=tmerc +lat_0=0 +lon_0=-73.5 +k=0.9999 +x_0=304800 +y_0=0 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## data source : in memory
## names : CAN_msk_alt
## values : 0.9513865, 173.2387 (min, max)